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Abstract For transient analysis of structural dynamics with reduced order model (ROM), data recovery procedures that use modal methods such as the classical mode-acceleration (MA) and modal-displacement (MD) methods are an important step in order to increase the convergence and accuracy of the solution. In this work, we propose novel MA and MD methods for highly accurate transient analysis with a reduced order model based on enhanced Craig–Bampton (ECB) formulation, which is an extension of the classical Craig–Bampton (CB) method that is a way to reduce the size of a finite element (FE) model. The performance of the proposed data recovery approach is demonstrated with two numerical examples. We also investigate the relation between the proposed and classical MA and MD methods. [ABSTRACT FROM AUTHOR]

Abstract A Novel Nodalized Reduced Order Model (NNROM) is developed in this paper to analyze the linear stability phenomena in a heated channel with supercritical water as a coolant. The existing models are based on finite volume approach, leading to a large number of non-linear time-dependent ODEs, making linear stability analysis (for infinitesimally perturbation) computationally expensive and tedious. Moreover, the non-linear stability analysis considers the effect of small but finite perturbations which becomes even more difficult. It is pointed out that the accuracy of the reduced order model developed here is not compromised, as the comparisons of the model results, with existing studies show good agreement. In ordered to develop the NNROM, the heated channel is divided into N number of nodes. The one-dimensional mass, energy and momentum conservation partial differential equations are converted into the corresponding time-dependent non-linear ordinary differential equations (ODEs) by applying the weighted residual method. The linear stability threshold of the system is determined by analyzing the eigenvalues of the Jacobian matrix at the steady states of the set of ODEs. Moreover, the linear stability boundary (Hopf bifurcation line) is represented in terms of trans-pseudo-critical phase change number ( N t p c ) , and pseudo-subcooling number ( N s p c ). A parametric study is done to identify the change in linear stability behavior of the system with the design parameters. Furthermore, non-linear stability analysis is carried out to identify Generalized Hopf (GH) bifurcation points in the N t p c − N s p c space. The GH points divide the stability boundary into sub-critical Hopf and super-critical Hopf parts, which is further varify by the numerical simulations. The identification of sub-critical region is quite important as it shows unstable limit cycles in the (linearly) stable region. Highlights • Novel Nodalized Reduced Order Model (NNROM) is developed for Supercritical water. • Single heated channel is nodalized into N numbers of node. • Non-linear stability analysis is carried out. • Sub-critical, super-critical and generalized hopf bifurcations is detected. • Qualitative change in stability behavior for design parameters is explained. [ABSTRACT FROM AUTHOR]

Abstract In recent years, the interest and demand for small satellites have grown exponentially. While in the past the end-of-life design for this type of spacecraft was often approximated or totally neglected, it has recently become increasingly important. Indeed, small spacecraft able to achieve advanced mission objectives are more frequently on the worldwide space agenda. They may contain components which might withstand the re-entry conditions and reach the ground. In addition, these spacecraft are usually limited to shallow re-entries which are more sensitive to atmospheric model uncertainties and thus have larger debris fields. The objective of this work is to provide a reliable and efficient statistical analysis to estimate the risk to aeronautic and maritime traffic as well as to ground based populations. A simple geometric safety assessment is proposed, based on the safety boxes concept introduced in the ESA Space Debris Mitigation Compliance Verification Guidelines. Correctly estimating the dimensions of a safety box and locating it over uninhabited regions, such as the oceans, guarantees a casualty risk below a prescribed value. Furthermore, by estimating the probability of debris landing outside the largest possible safety box within which there is a zero casualty risk, the maximum probability of control failure admissible for the mission can be estimated. This proposed safety analysis is achieved using two re-entry models of differing complexity. The high fidelity model includes both the aerodynamic and aerothermodynamic effects that occur during re-entry and is used to statistically characterize "high level" uncertain variables such as the ballistic coefficient and the demise altitude. The reduced order model is based on these high level variables and captures the spacecraft fragmentation behavior and its re-entry dynamics with significantly less computation time than the high fidelity model. Coupled with advanced statistical techniques designed to estimate very low probabilities such as the Inputs' Statistics Method, a reliable safety analysis can be conducted with a limited overall computational burden. The proposed safety analysis is applied to a fictitious 2U CubeSat mission that performs a controlled re-entry using the Drag De-orbit Device developed by the ADAMUS laboratory at the University of Florida. Highlights • Novel application of the inputs' statistics method to re-entry of small satellites. • Computation of safety box for CubeSat parts impact greatly reduced. • Alternative to tightly controlled state of the art tools from ESA and NASA. [ABSTRACT FROM AUTHOR]

Abstract Wave energy converters (WECs) face difficulties such as low operating range, low power output and, fluctuating power. A seamless synchronization among WEC components is required to get a better performance. For control system studies, the model should capture all the necessary dynamics involved in each conversion stages, however the interlinked complexity in each subsystem increases the computation time. This article presents a reduced order wave-to-wire (WTW) model of an oscillating water column (OWC) based WEC. The approach involves modeling of hydrodynamic and aerodynamic coupling of the capture chamber, aerodynamic and thermodynamic coupling inside the capture chamber, aerodynamic and rotor dynamic coupling in air turbine; and rotor dynamics and generator dynamics in the turbine generator coupling. The result shows that the model retains its fundamental dynamics and reduces the number of unknowns to describe the state space. The model indicates the correlation of each variable represented in the state space. The model predicted power output for different sea state. It also shows that the accuracy and the efficiency of the model are acceptable for OWC-WEC control system studies. The present model can be used as a time domain tool to design an effective control system for OWC device for different sea states, and the overall device performance can be improved significantly. [ABSTRACT FROM AUTHOR]

Abstract A new reduced order model (ROM) provides rapid and reasonably accurate prediction of the complex behavior of multiple, simultaneously growing radial hydraulic fractures. The method entails vastly reducing the degrees of freedom typically associated with fully-coupled simulations of this multiple moving boundary problem by coupling together an approximation of the influence of the stress interaction among the fractures ("stress shadow") with an approximation of fluid flow and elasticity, ensuring preservation of global volume balance, global energy balance, elasticity, and compatibility of the crack opening with the inlet fluid flux. Validating with large scale ("high-fidelity") simulations shows the ROM solution captures not only the basic suppression of interior hydraulic fractures in a uniformly-spaced array due to the well-known stress shadowing phenomenon, but also complex behaviors arising when the spacing among the hydraulic fractures is non-uniform. The simulator's usefulness is demonstrated through a proof-of-concept optimization whereby non-uniform spacing and stage length are chosen to maximize the fracture surface area and/or the uniformity of growth associated with each stimulation treatment. Highlights • Consideration of multiple radial hydraulic fractures. • Rapidly computing yet sufficiently accurate approximation. • Demonstrates fluid flow approximation capturing similar energy dissipation. • Preserves global fluid volume balance, propagation, and elasticity. • Enables optimization requiring thousands of model evaluations. [ABSTRACT FROM AUTHOR]

In this paper, we consider an important problem for modeling complex coupled phenomena in porous media at multiple scales. In particular, we consider flow and transport in the void space between the pores when the pore space is altered by new solid obstructions formed by microbial growth or reactive transport, and we are mostly interested in pore-coating and pore-filling type obstructions, observed in applications to biofilm in porous media and hydrate crystal formation, respectively. We consider the impact of these obstructions on the macroscopic properties of the porous medium, such as porosity, permeability and tortuosity, for which we build an experimental probability distribution with reduced models, which involves three steps: (1) generation of independent realizations of obstructions, followed by, (2) flow and transport simulations at pore-scale, and (3) upscaling. For the first step, we consider three approaches: (1A) direct numerical simulations (DNS) of the PDE model of the actual physical process called BN which forms the obstructions, and two non-DNS methods, which we call (1B) CLPS and (1C) LP. LP is a lattice Ising-type model, and CLPS is a constrained version of an Allen–Cahn model for phase separation with a localization term. Both LP and CLPS are model approximations of BN, and they seek local minima of some nonconvex energy functional, which provide plausible realizations of the obstructed geometry and are tuned heuristically to deliver either pore-coating or pore-filling obstructions. Our methods work with rock-void geometries obtained by imaging, but bypass the need for imaging in real-time, are fairly inexpensive, and can be tailored to other applications. The reduced models LP and CLPS are less computationally expensive than DNS, and can be tuned to the desired fidelity of the probability distributions of upscaled quantities.

We investigate data-driven, simple-to-implement residential environmental models that can serve as the basis for energy saving algorithms in both retrofits and new designs of residential buildings. Despite the nonlinearity of the underlying dynamics, using Koopman operator theory framework in this study we show that a linear second order model embedding, that captures the physics that occur inside a single or multi zone space does well when compared with data simulated using EnergyPlus. This class of models has low complexity. We show that their parameters have physical significance for the large-scale dynamics of a building and are correlated to concepts such as the thermal mass. We investigate consequences of changing the thermal mass on the energy behavior of a building system and provide best practice design suggestions.

A Resonance calculation using energy Spectral Expansion (RSE) method has been recently proposed in order to efficiently treat complicated heterogeneous geometry and resonance interference effect. In the RSE method, ultra-fine group spectra are generated from ultra-fine group calculations in homogeneous geometry, and the spectra are expanded by the orthogonal basis on energy based on the singular value decomposition. Then the transport calculation for expansion coefficients is numerically performed, and the ultra-fine group spectra in the target heterogeneous regions are reconstructed by the expansion coefficients and the orthogonal basis. In this study, the RSE method is applied to multi-cell geometries including UO2, MOX and water cells, in which the resonance interference effect between UO2 and MOX fuel cells appears. The validity of the RSE method is confirmed through comparison with the reference effective multi-group cross sections obtained from the direct ultra-fine group calculation in the target heterogeneous geometry.

• A rapid method based on proper orthogonal decomposition and radial basis function is presented for wheel fatigue evaluation. • The computational efficiency in predicting wheel fatigue life under biaxial load spectrum is significantly improved. • The accuracy of the method in the calculation of wheel stresses and fatigue life is proven by experimental results. This paper presents a rapid method for predicting the biaxial fatigue life of automotive wheels using a combination of proper orthogonal decomposition and radial basis function algorithm. Currently, numerical simulations of biaxial fatigue tests are being developed to evaluate wheel performance. However, these simulations are computationally expensive due to the need to simulate multiple discrete loading cases within a given biaxial spectrum. To address this issue, we propose a novel approach that utilizes proper orthogonal decomposition and radial basis function algorithm to improve computational efficiency. By leveraging high-fidelity simulation results from a small number of loading cases, a reduced order model is constructed to accurately predict the tire-rim interface force fields required for wheel strength calculations. The reduced order model significantly reduces the computational time by 65.4% for simulating all loading cases, while maintaining a maximum predicted error of less than 2% compared to the high-fidelity model. Subsequently, the predicted interface forces are mapped onto the rim surface for strength calculation, and the wheel fatigue life is determined using the Brown-Miller multiaxial damage criterion. Comparative analysis with experimental results demonstrates the desirable accuracy of our method in simulating the stress-strain history, crack initiation position, and minimum fatigue life of the wheel. Overall, the proposed method offers a powerful tool for the rapid fatigue analysis of spectrum-loaded wheels, providing an efficient and accurate means of predicting biaxial fatigue life. [ABSTRACT FROM AUTHOR]

We present a model reduction approach that extends the original empirical interpolation method to enable accurate and efficient reduced basis approximation of parametrized nonlinear partial differential equations (PDEs). In the presence of nonlinearity, the Galerkin reduced basis approximation remains computationally expensive due to the high complexity of evaluating the nonlinear terms, which depends on the dimension of the truth approximation. The empirical interpolation method (EIM) was proposed as a nonlinear model reduction technique to render the complexity of evaluating the nonlinear terms independent of the dimension of the truth approximation. We introduce a first-order empirical interpolation method (FOEIM) that makes use of the partial derivative information to construct an inexpensive and stable interpolation of the nonlinear terms. We propose two different FOEIM algorithms to generate interpolation points and basis functions. We apply the FOEIM to nonlinear elliptic PDEs and compare it to the Galerkin reduced basis approximation and the EIM. Numerical results are presented to demonstrate the performance of the three reduced basis approaches. • A first-order empirical interpolation method is developed for model reduction of nonlinear parametrized PDEs. • The method makes use of partial derivatives to construct interpolation points and basis functions. • The method yields accurate and efficient reduced basis approximations for nonlinear elliptic PDEs. • Numerical results are presented to assess the method relative to other reduced basis approaches. [ABSTRACT FROM AUTHOR]

The investigation of fluid-solid systems is very important in a lot of industrial processes. From a computational point of view, the simulation of such systems is very expensive, especially when a huge number of parametric configurations needs to be studied. In this context, we develop a non-intrusive data-driven reduced order model (ROM) built using the proper orthogonal decomposition with interpolation (PODI) method for Computational Fluid Dynamics (CFD) - Discrete Element Method (DEM) simulations. The main novelties of the proposed approach rely in (i) the combination of ROM and FV methods, (ii) a numerical sensitivity analysis of the ROM accuracy with respect to the number of POD modes and to the cardinality of the training set and (iii) a parametric study with respect to the Stokes number. We test our ROM on the fluidized bed benchmark problem. The accuracy of the ROM is assessed against results obtained with the FOM both for Eulerian (the fluid volume fraction) and Lagrangian (position and velocity of the particles) quantities. We also discuss the efficiency of our ROM approach. • Development of a data-driven ROM for a CFD-DEM framework. • Combination of ROM and FV methods for multiphysics problems. • Extensive numerical investigation of the ROM error. • Use of local and global PODI techniques for physical parametrization. • Validation against a relevant benchmark for pharmaceutical industry. [ABSTRACT FROM AUTHOR]

• A reduced-order model was employed to reconstruct the pebble bed and pore flow. • Original snapshots were obtained through high-fidelity CFD-DEM methods. • The computation time is drastically reduced while the accuracy is guaranteed. • Rapid acquisition of pressure and flow characteristics of helium properties based on ROM results. • Based on ROM results, the influencing factors of the effective thermal conductivity of the pebble bed were analyzed. In recent years, the pebble bed module has garnered increased attention due to its inherent safety and versatile applications, particularly in the form of High-Temperature Gas-Cooled reactors and fusion tritium breeding blankets. Understanding the thermal–hydraulic characteristics within the pebble bed is crucial for the safety evaluation and design of such reactors. To study pore flow in the pebble bed, discrete element coupling methods and computational fluid dynamics (DEM-CFD) are commonly employed. However, simulating thousands of pebbles can be computationally intensive and time-consuming. To address this, reduced order models (ROMs) have been developed to reduce the computational complexity by employing simplified systems instead of the original complex system, thereby significantly saving computational time while maintaining accuracy. In this work, ROMs have been established for body-centered cubic packing, face-centered cubic packing, and randomly packed beds of pebbles. Using the ROM results, subsequent analysis focused on two important thermal–hydraulic characteristics: pressure and effective thermal conductivity. A comparison was made between the results obtained from the full-order model (FOM) using CFD and the reconstructed ROM results. The case studies demonstrate the potential of the proposed approach in rapidly and accurately investigating significant flow and heat transfer features, such as pressure and temperature. [ABSTRACT FROM AUTHOR]

The optimal design of heat sink using Moving Morphable Components (MMC) is presented for natural convection problems. The topology optimization design of the heat sink has a heavy computational burden. For one thing, the multi-physics model is a fully coupled nonlinear system, and for another, a large number of degrees of freedom (DOF) of the design variables are involved in the optimization process. The governing equations of the multi-physics model are composed of the incompressible Navier-Stokes equations related to velocity and pressure and the heat transfer equation related to temperature. A reduced-order model that simplifies physical quantities is introduced to reduce the number of state variables, and the Gaussian Seidel iteration algorithm is used to further reduce computing scale. Compared with the density-based topology optimization, the MMC-based topology optimization shows similar heat sink design through fewer design variables and good heat dissipation performance. In addition, the heat sink structure with fully explicit boundary information is obtained. The numerical results show that the number of components and the lower bounds of the components have an effect on the heat dissipation performance. As the number of components increases, the heat dissipation performance improves. However, when the number of components reaches a certain level, the heat dissipation performance reaches saturation. Moreover, the higher the processing accuracy of the mechanical equipment, the smaller the lower bounds of the components that can be designed, and the better the heat dissipation performance. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel reduced order model (ROM) lengthscale that is constructed by using energy distribution arguments. The new energy-based ROM lengthscale is fundamentally different from the current ROM lengthscales, which are built by using dimensional arguments. To assess the novel, energy-based ROM lengthscale, we compare it with a standard, dimensionality-based ROM lengthscale in two fundamentally different types of models: (i) the mixing-length ROM (ML-ROM), which is a ROM closure model; and (ii) the evolve-filter-relax ROM (EFR-ROM), which is a regularized ROM. We test the four combinations (i.e., ML-ROM and EFR-ROM equipped with the energy-based and dimensionality-based lengthscales) in the numerical simulation of the turbulent channel flow at R e τ = 395. The numerical investigation yields the following conclusions: (i) The new energy-based ROM lengthscale is significantly (almost two orders of magnitude) larger than the standard dimensionality-based ROM lengthscale. As a result, the energy-based lengthscale yields more stable ML-ROMs and EFR-ROMs than the dimensionality-based lengthscale. (ii) The energy-based lengthscale displays the correct asymptotic behavior with respect to the ROM dimension, whereas the dimensionality-based lengthscale does not. The energy-based lengthscale is intrinsically adaptive with respect to the ROM dimension, which is important in realistic settings where using the full order model data to determine an optimal ROM lengthscale may not be possible. (iii) The energy-based lengthscale yields ML-ROMs and (when significant filtering is effected) EFR-ROMs whose parameters are less sensitive (i.e., more robust) than the parameters of the ML-ROMs and EFR-ROMs based on the dimensionality-based lengthscale. The novel energy-based lengthscale could enable the development of better scale-aware ROM strategies for flow-specific applications and is expected to have long term applications in nuclear reactor thermal-hydraulics. • Novel reduced order model (ROM) lengthscale built by using energy distribution arguments. • The new and standard lengthscales compared in the mixing-length ROM and evolve-filter-relax ROM. • The new lengthscale is significantly larger than the standard lengthscale. • The new lengthscale is asymptotically sound, whereas the standard lengthscale is not. • The new lengthscale is less sensitive (more robust) than the standard lengthscale. [ABSTRACT FROM AUTHOR]

In this work, the self-consistent clustering analysis (SCA) framework is extended to include homogenization and full field analysis of 3D anisotropic woven composite Representative Unit Cell (RUC). The developed extended framework has two new features, namely, (i), to reconstruct the local field variables, a strain refinement stage is presented by solving full field Lippmann–Schwinger equations within 3D anisotropic woven composite RUC following the online predictive stage in SCA, and (ii), discrete Green's operator based on finite difference is adopted to improve the accuracy of refined point-wise physical field variables. To demonstrate the accuracy and efficiency of the proposed method, benchmark problems are analyzed, and results are compared to directly numerical simulation (DNS). For the reproducibility of presented results, the developed code can be freely downloaded from https://github.com/Tong-RuiLiu/Extended-SCA-and-FFT-based-strain-refinement-method-. • 1st time SCA with strain refinement stage is proposed for 3D woven composite RUC. • 1st time performance of discrete Green's operator is investigated in SCA. • Cause & effect analysis is carried for the convergence and accuracy of results. • Minimal change of code is needed from FFT homogenization and SCA. [ABSTRACT FROM AUTHOR]

The high dimensions and governing non-linear dynamics in wind farm systems make the design of numerical optimal controllers computationally expensive. A possible pathway to circumvent this challenge lies in finding reduced order models which can accurately embed the existing non-linearities. The work presented here applies the ideas motivated by non-linear dynamical systems theory—the Koopman Operator—to an innovative algorithm in the context of wind farm systems—Input Output Dynamic Mode Decomposition (IODMD)—to improve on the ability to model the aerodynamic interaction between wind turbines in a wind farm and uncover insights into the existing dynamics. It is shown that a reduced order linear state space model can reproduce the downstream turbine generator power dynamics and reconstruct the upstream turbine wake. It is further shown that the fit can be improved by judiciously choosing the Koopman observables used in the IODMD algorithm without jeopardizing the models ability to rebuild the turbine wake. The extensions to the IODMD algorithm provide an important step towards the design of linear reduced order models which can accurately reproduce the dynamics in a wind farm.

Current technology in evaluating the aeroelastic behavior of aerospace structures is based on the staggered coupling between structural and low fidelity linearized aerodynamic solvers, which has inherent limitations, although tried and trusted outside the transonic region. These limitations arise from the assumptions in the formulation of linearized aerodynamics and the lower fidelity in the description of the flowfield surrounding the structure. The validity of low fidelity aerodynamics also degrades fast with the deviation from a typical aerodynamic shape due to the inclusion of various control devices, gaps, or discontinuities. As innovative wings tend to become more flexible and also include a variety of morphing devices, it is expected that using low fidelity linearized aerodynamics in aeroelastic analysis will tend to induce higher levels of uncertainty in the results. An obvious solution to these issues is to use high fidelity aerodynamics. However, using high fidelity aerodynamics incurs a very high computational cost. Various formulations of reduced order models have shown promising results in reducing the computational cost. In the present work, the static aeroelastic behavior of three characteristic aeroelastic problems is obtained using both a full three-dimensional staggered coupled scheme and a time domain Volterra series based reduced order model (ROM). The reduced order model’s ability to remain valid for a wide range of dynamic pressures around a specific Mach number (and Reynolds number regime if viscous flow is considered) and the capability to modify structural parameters such as damping ratios and natural frequencies are highlighted.

The aim of this study was to elaborate and validate a reduced order model able to forecast solar heat gains as a function of the architectural parameters that determine the solar heat gains. The study focused on office buildings in Catalonia and Spain and their physical values were taken from the Spanish Building Technical Code and European Union Directive 2018/844. A reduced order model with three direct variables (solar heat gain coefficient, shade factor, window to wall ratio) and one indirect design variable (building orientation) was obtained and validated in respect to the International Performance Measurement and Verification Protocol. Building envelope properties were fixed and the values were taken from the national standards of Spain. This work validates solar heat gain coefficient as a primary variable in determining the annual solar heat gains in a building. Further work of developed model could result in building energy need quick evaluation tool in terms of solar heat gains for architects in building early stage as it has an advantage over detailed building simulation programs in terms of instant calculation and the limited need for predefined input data.

Developing accurate, efficient, and robust closure models is essential in the construction of reduced order models (ROMs) for realistic nonlinear systems, which generally require drastic ROM mode truncations. We propose a deep residual neural network (ResNet) closure learning framework for ROMs of nonlinear systems. The novel ResNet-ROM framework consists of two steps: (i) In the first step, we use ROM projection to filter the given nonlinear system and construct a spatially filtered ROM. This filtered ROM is low-dimensional, but is not closed. (ii) In the second step, we use ResNet to close the filtered ROM, i.e., to model the interaction between the resolved and unresolved ROM modes. We emphasize that in the new ResNet-ROM framework, data is used only to complement classical physical modeling (i.e., only in the closure modeling component), not to completely replace it. We also note that the new ResNet-ROM is built on general ideas of spatial filtering and deep learning and is independent of (restrictive) phenomenological arguments, e.g., of eddy viscosity type. The numerical experiments for the 1D Burgers equation show that the ResNet-ROM is significantly more accurate than the standard projection ROM. The new ResNet-ROM is also more accurate and significantly more efficient than other modern ROM closure models.

The galvano mirror has been widely used in the field of laser processing. It has a variety of vibration modes which are due to the torsion of the motor and the elastic deformation of the mirror. To improve the mechanical structure and to identify the resonance causes, the model of the galvano mirror is constructed. Moreover, the lumped mass system model is parametrical considered to verify the relationship between each resonance frequency and the component of the galvano mirror. The galvano mirror is composed of the motor, the coupling, and the mirror. Then, the models of each part are separately constructed and finally connected to build the model of the galvano mirror. In detail, the motor model is constructed based on the torsion of the motor itself. The mirror model which is regarded as the elastic structure is constructed based on the reduced order model. The galvano mirror model includes the pitching vibration mode which is not able to be actually detected by encoder. Any parameters of the model which are able to be used for future improvements from the mechanical point of view are changed to verify the rate of change against each resonance. In addition, the coupling rigidity is changed to shift the resonances to high frequency region through various approaches and to verify the propriety of the model.

We apply a modified proper orthogonal decomposition (POD) to large eddy simulation data of a wind turbine wake in a turbulent atmospheric boundary layer. The turbine is modeled as an actuator disk. Our analysis mainly focuses on the pragmatic identification of spatial modes, which yields a low order description of the wake flow. This reduction to a few degrees of freedom is a crucial first step for the development of simplified dynamic wake models based on modal decompositions. It is shown that only a few modes are necessary to capture the basic dynamical aspects of quantities that are relevant to a turbine in the wake flow. Furthermore, we show that the importance of the individual modes depends on the relevant quantity chosen. Therefore, the optimal choice of modes for a possible model could in principle depend on the application of interest. We additionally present a possible interpretation of the extracted modes by relating them to the specific properties of the wake. For example, the first mode is related to the horizontal large-scale movement.

The estimation of fluid flows inside a centrifugal pump in realtime is a challenging task that cannot be achieved with long-established methods like CFD due to their computational demands. We use a projection-based reduced order model (ROM) instead. Based on this ROM, a realtime observer can be devised that estimates the temporally and spatially resolved velocity and pressure fields inside the pump. The entire fluid-solid domain is treated as a fluid in order to be able to consider moving rigid bodies in the reduction method. A greedy algorithm is introduced for finding suitable and as few measurement locations as possible. Robust observability is ensured with an extended Kalman filter, which is based on a time-variant observability matrix obtained from the nonlinear velocity ROM. We present the results of the velocity and pressure ROMs based on a unsteady Reynolds-averaged Navier-Stokes CFD simulation of a 2D centrifugal pump, as well as the results for the extended Kalman filter., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 The Authors. Published by Elsevier Ltd.)

Summary: Reduced order models (ROMs) are becoming increasingly useful for saving computational cost in response prediction of vibrating systems. In a number of applications such as uncertainty quantification, ROMs require robustness over a wide variation of parameters. Accordingly, often they are classified as local and global, based on their performance in the parametric domain. Availability of an error bound of a ROM helps in achieving this robustness, mainly by allowing adaptivity. In this work, for a linear random dynamical system, first, an a posteriori error bound is developed based on the residual in the governing differential equation. Next, based on this error bound, two adaptive methods are proposed for building robust ROMs, that is, one for local, and another for global. While both methods are based on a greedy search approach, a modification is proposed in the training stage of the global ROM for accelerated convergence. These methods are then applied to an uncertainty quantification problem in a statistical simulation framework, and accordingly, two algorithms are developed. A detailed numerical study on vibration of a bladed disk assembly is conducted to study the accuracy and efficiency of the proposed error bound and adaptive ROMs. It is found that these adaptive ROMs provide a considerable speed‐up in estimating the probability of failure. [ABSTRACT FROM AUTHOR]

Crystal plasticity simulation is a widely used technique for studying the deformation processing of polycrystalline materials. However, inclusion of crystal plasticity simulation into design paradigms such as integrated computational materials engineering (ICME) is hindered by the computational cost of large-scale simulations. In this work, we present a machine learning (ML) framework using the material information platform, Open Citrination, to develop and calibrate a reduced order crystal plasticity model for face-centered cubic (FCC) polycrystalline materials, which can be both rapidly exercised and easily inverted. The reduced order model takes crystallographic texture, constitutive model parameters, and loading condition as inputs and returns the stress-strain curve and final texture. The model can also be inverted and take a stress-strain curve, loading condition, and final texture as inputs and return the initial texture and constitutive model parameters as outputs. Principal component analysis (PCA) is used to develop an efficient description of the crystallographic texture. A viscoplastic self-consistent (VPSC) crystal plasticity solver is used to create the training data by modeling the stress-strain behavior and evolution of texture during deformation processing. [ABSTRACT FROM AUTHOR]

Abstract The variable-stiffness fiber composite plates which have an enhanced design flexibility, largely rely on laminate optimizations to maximize the buckling performance. The corresponding computational efficiency becomes a key issue, in particular when the nonlinear structural behavior is considered. The finite element method based on a full nonlinear analysis is a standard technique for nonlinear structural analysis, however the high computational complexities generated from both the incremental-iterative procedure and the very refined mesh needed for the discrete modeling of curved fibers, are still a decisive cost factor on modern computers. In this work, the Koiter-Newton method is further extended to nonlinear buckling analysis, including the pre and post buckling stage, of variable stiffness composite plates. A four-node quadrilateral element based on the classical laminated plate theory is developed in framework of the von Kármán kinematics, for the finite element implementation of the proposed asymptotic method. The reduced order model, with or without imperfections, is constructed using the improved Koiter's asymptotic expansion, for both the symmetrical and unsymmetrical laminates. The nonlinear response curve of loaded structure can be traced automatically, using the nonlinear predictor and corrections both generated from the reduced order model. This leads to a fairly large step size in the path-tracing process, compared to that for the classical Newton method. The reduced order model largely reduces the computational burden produced by the high-density FE mesh for the varied fiber path. Numerical results indicate the overall high quality and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

The operation range of today’s micro-electromechanical systems (MEMS) continues to enter the geometric nonlinear regime due to miniaturization and performance requirements. One example is the MEMS Coriolis Vibratory Gyroscope (CVG), where the drive mode operates beyond the structural width, causing a change in resonance frequency upon displacement amplitude. Getting good estimates for this change in frequency has been a major issue in the development of CVGs over the past 20 years. In this paper, we present simulation methods and strategies to extract the nonlinear frequencies of such actuated MEMS from the finite element model of the device. The methods are explained in detail and benchmarked with two MEMS structures. As result, we find that the new methods fulfill the accuracy and performance requirements to aid MEMS designers in developing and optimizing the mechanical structure of their devices. [2018-0136] [ABSTRACT FROM AUTHOR]

This article deals with the nonlinear eigenvalue problem originating from the finite element discretization of mechanical structures involving linear viscoelastic material. The material function is assumed to be positive real, which allows a location of the eigenvalues in the left complex half space of the Laplace domain. The solution method for the considered nonlinear eigenvalue problem is based on the contour integral method, where special focus is put on the efficient numerical computation of the linear system along the boundary of the given search area. For this purpose, the reduced order model technique is used and appropriate a priori error estimates are provided. Finally, the validity of the proposed method is illustrated in numerical examples. [ABSTRACT FROM AUTHOR]

The paper focuses on a coupled Bayesian-Proper Generalized Decomposition (PGD) approach for the real-time identification and updating of numerical models. The purpose is to use the most general case of Bayesian inference theory in order to address inverse problems and to deal with different sources of uncertainties (measurement and model errors, stochastic parameters). In order to do so with a reasonable CPU cost, the idea is to replace the direct model called for Monte-Carlo sampling by a PGD reduced model, and in some cases directly compute the probability density functions from the obtained analytical formulation. This procedure is first applied to a welding control example with the updating of a deterministic parameter. In the second application, the identification of a stochastic parameter is studied through a glued assembly example. [ABSTRACT FROM AUTHOR]

Pulverized coal is injected into blast furnace tuyeres to reduce coke consumption as well as to reduce hot metal production cost. Knowledge of the combustion behavior of pulverized coal in the blast furnace raceway zone and accumulation of unburnt char are of paramount importance. To alleviate the problem of high computational time of a multidimensional model, a reduced order raceway model of the blast furnace has been proposed for real time plant application. The model is capable of predicting radial temperature and gas composition profiles in the raceway zone with and without pulverized coal injection (PCI). Influence of all the key operating process parameters such as PCI rate, blast temperature, blast volume, oxygen enrichment and steam addition on the raceway combustion behavior, temperature and gas composition profiles as well as raceway depth have been investigated and validated with literature and plant database, wherever possible. It has been observed that with increasing PCI rate on a fixed fuel rate basis, the peak gas temperature (PGT) decreases and the location of PGT tends to shift toward tuyere nose. The present model is an efficient computational tool to predict the raceway process variables for online application, in synchronization with plant operation. [ABSTRACT FROM AUTHOR]

The power flow model performs the analysis of electric distribution and transmission systems. With this statement at hand, in this work we present a summary of those solvers for the power flow equations, in both algebraic and parametric version. The application of the Alternating Search Direction method to the power flow problem is also detailed. This results in a family of iterative solvers that combined with Proper Generalized Decomposition technique allows to solve the parametric version of the equations. Once the solution is computed using this strategy, analyzing the network state or solving optimization problems, with inclusion of generation in real-time, becomes a straightforward procedure since the parametric solution is available. Complementing this approach, an error strategy is implemented at each step of the iterative solver. Thus, error indicators are used as an stopping criteria controlling the accuracy of the approximation during the construction process. The application of these methods to the model IEEE 57-bus network is taken as a numerical illustration. [ABSTRACT FROM AUTHOR]

The objective of this article is to introduce a new method including model order reduction for the life prediction of structures subjected to cycling damage. Contrary to classical incremental schemes for damage computation, a non-incremental technique, the LATIN method, is used herein as a solution framework. This approach allows to introduce a PGD model reduction technique which leads to a drastic reduction of the computational cost. The proposed framework is exemplified for structures subjected to cyclic loading, where damage is considered to be isotropic and micro-defect closure effects are taken into account. A difficulty herein for the use of the LATIN method comes from the state laws which can not be transformed into linear relations through an internal variable transformation. A specific treatment of this issue is introduced in this work. [ABSTRACT FROM AUTHOR]

We investigate the chaotic dynamics of micro- and nanoelectromechanical (MEMS/NEMS) beam resonators actuated electrostatically by two-sided electrodes, considering devices with realistic physical parameters. We model the resonators using the Euler–Bernoulli beam theory with the addition of viscous damping, midplane stretching and the electrostatic force. For the purpose of numerical simulations, the partial differential equation describing the system is reduced to a one degree of freedom model using the Galerkin method. The resulting nonlinear ordinary differential equation incorporates the main effects of the beam curvature. A comparison with the widely used parallel plate approximation (PPA) evidences the significant effects of the beam curvature. It is also concluded that in the case of resonators with two-sided electrodes special care must be taken when using the PPA. A detailed numerical analysis reveals the region in the relevant parameter space where chaos can be found. Phase portraits, Poincaré sections and bifurcation diagrams are used to characterize the chaotic attractors. The effects of gap asymmetry and damping are also investigated, showing that a stronger chaotic dynamics is favored by small asymmetries and smaller damping. In general, a more complex chaotic dynamics was found, compared to what was initially expected. The results are relevant in view of the potential practical applications in the generation of pseudo-random numbers and chaotic signals for secure communications. The proposed improved model can be easily implemented numerically, helping in the design and simulation of resonators, and the comparison between theoretical and experimental results. [ABSTRACT FROM AUTHOR]

Electrical high voltage (HV) machines are prone to corona discharges leading to power losses as well as damage of the insulating layer. Many different techniques are applied as corona protection and computational methods aid to select the best design. In this paper we develop a reduced-order model in 1D estimating electric field and temperature distribution of a conductor wrapped with different layers, as usual for HV-machines. Many assumptions and simplifications are undertaken for this 1D model, therefore, we compare its results to a direct numerical simulation in 3D quantitatively. Both models are transient and nonlinear, giving a possibility to quickly estimate in 1D or fully compute in 3D by a computational cost. Such tools enable understanding, evaluation, and optimization of corona shielding systems for multilayered coils. [ABSTRACT FROM AUTHOR]

Charge transfer and mass transport are two underlying mechanisms which are coupled in desalination dynamics using capacitive deionization (CDI). We developed simple reduced-order models based on a mixed reactor volume principle which capture the coupled dynamics of CDI operation using closed-form semi-analytical and analytical solutions. We use the models to identify and explore self-similarities in the dynamics among flow rate, current, and voltage for CDI cell operation including both charging and discharging cycles. The similarity approach identifies the specific combination of cell (e.g. capacitance, resistance) and operational parameters (e.g. flow rate, current) which determine a unique effluent dynamic response. We here demonstrate self-similarity using a conventional flow between CDI (fbCDI) architecture, and we hypothesize that our similarity approach has potential application to a wide range of designs. We performed an experimental study of these dynamics and used well-controlled experiments of CDI cell operation to validate and explore limits of the model. For experiments, we used a CDI cell with five electrode pairs and a standard flow between (electrodes) architecture. Guided by the model, we performed a series of experiments that demonstrate natural response of the CDI system. We also identify cell parameters and operation conditions which lead to self-similar dynamics under a constant current forcing function and perform a series of experiments by varying flowrate, currents, and voltage thresholds to demonstrate self-similarity. Based on this study, we hypothesize that the average differential electric double layer (EDL) efficiency (a measure of ion adsorption rate to EDL charging rate) is mainly dependent on user-defined voltage thresholds, whereas flow efficiency (measure of how well desalinated water is recovered from inside the cell) depends on cell volumes flowed during charging, which is determined by flowrate, current and voltage thresholds. Results of experiments strongly support this hypothesis. Results show that cycle efficiency and salt removal for a given flowrate and current are maximum when average EDL and flow efficiencies are approximately equal. We further explored a range of CC operations with varying flowrates, currents, and voltage thresholds using our similarity variables to highlight trade-offs among salt removal, energy, and throughput performance. [ABSTRACT FROM AUTHOR]

Many industrial applications benefit from predictive computer simulation to reduce costs and time, and shorten product development cycle. Computational multibody system dynamics formalisms and software tools have proved to be particularly useful in the simulation of machinery and mechanical systems. Nowadays, however, the complexity of the applications under study often makes it necessary to consider the interaction of mechanical systems with other components of different nature, physical behaviour, and time scale, such as hydraulics or electronics. Co-simulation is an increasingly important approach to formulate and solve the dynamics of these multiphysics setups. In these, modelling techniques and solvers that are tailored to the requirements of each subsystem execute in parallel and are coupled via the exchange of a limited number of inputs and outputs at certain communication times. Co-simulation has clear potential in the modelling of complex engineering systems. On the other hand, there are also challenges. The use of co-simulation may compromise the stability of the numerical solution, especially when non-iterative coupling schemes are used. In this work, we introduce a modelling technique to improve the dynamic interfacing of mechanical systems in co-simulation setups, based on a reduced representation of multibody systems. This reduced order model is used to obtain a physically meaningful prediction of the evolution of the multibody subsystem dynamics that enables the improvement of the solution of other subsystems. The technique is illustrated in the co-simulation of some examples that include both mechanical and hydraulic components. Results show that dynamic interfaces based on reduced models can be used to improve the stability of non-iterative co-simulation schemes in multiphysics engineering systems, enabling the use of larger communication step-sizes. [ABSTRACT FROM AUTHOR]

Monitoring is a crucial aspect of geologic carbon dioxide (CO 2 ) sequestration risk management. Effective monitoring is critical to ensure CO 2 is safely and permanently stored throughout the life-cycle of a geologic CO 2 sequestration project. Effective monitoring involves deciding: (i) where is the optimal location to place the monitoring well(s), and (ii) what type of data (pressure, temperature, CO 2 saturation, etc.) should be measured taking into consideration the uncertainties at geologic sequestration sites. We have developed a filtering-based data assimilation procedure to design effective monitoring approaches. To reduce the computational cost of the filtering-based data assimilation process, a machine-learning algorithm: Multivariate Adaptive Regression Splines is used to derive computationally efficient reduced order models from results of full-physics numerical simulations of CO 2 injection in saline aquifer and subsequent multi-phase fluid flow. We use example scenarios of CO 2 leakage through legacy wellbore and demonstrate a monitoring strategy can be selected with the aim of reducing uncertainty in metrics related to CO 2 leakage. We demonstrate the proposed framework with two synthetic examples: a simple validation case and a more complicated case including multiple monitoring wells. The examples demonstrate that the proposed approach can be effective in developing monitoring approaches that take into consideration uncertainties. [ABSTRACT FROM AUTHOR]

Industrials have an intensive use of numerical simulations in order to avoid physical testing and to speed up the design stages of their products. The numerical testing is indeed quicker to set-up, less expensive, and supplies a lot of information about the system under study. Moreover, it can be much closer to the physical tests as the computation power increases. Despite the rise of this power, time consuming simulations remain challenging to be used in design process, especially in an optimization study. Crash simulations belong to this category. These rapid dynamic computations are used by RENAULT during the sizing of the vehicle structure in order to ensure that it meets specifications set up to reach safety criteria in case of accidents. They are completed using finite element software such as VPS (Virtual Performance Solver) developed by ESI group that will be used in this study. For car manufacturers, the goal of the optimization study is to minimize the mass of the vehicle (and thus its consumption) by modifying the thicknesses of some parts (from 20 to 100 variables). Industrials such as RENAULT currently perform optimization studies based on numerical design of experiments. The number of computations required by this technique is from 3 to 10 times the number of variables. This is too much in order to be intensively used in a design process. In order to decrease the time-to-market and to explore alternative technical solutions, we explore the potential of using a parametrized reduced order model in the optimization studies. The parametrized reduced order model gives an estimation of the high-fidelity result for a new set of parameters without using the solver, by analysing the existing results of previous computations with various sets of parameters. The developed reduced order model is called ReCUR. It is partly based on a CUR approach embedded in a regression analysis. The regression statistical model uses the data of a few calculations made with the solver. Other tools such as clustering and linear programming are used to get the regression analysis more efficient. It is hoped to drastically reduce the number of required simulations of a standard optimization study. In this paper, the construction of the reduced order model will be presented. Then, the relevancy of using the reduced order model into a design process will be exhibited through the treatment of two industrial test-cases. Some improvements of the method as well as several potential uses will then be outlined. The applications will highlight the promising power of the method to shorten design process using optimization and long-run simulations. [ABSTRACT FROM AUTHOR]

Uncertainty quantification is an emerging research area aiming at quantifying the variation in engineering system outputs due to uncertain inputs. One approach to study problems in uncertainty quantification is using polynomial chaos expansions. Though, a well-known limitation of polynomial chaos approaches is that their computational cost becomes prohibitive when the dimension of the stochastic space is large. In this paper, we propose a procedure to solve high dimensional stochastic problems with a limited computational budget. The methodology is based on an existing non-intrusive model reduction scheme for polynomial chaos representation, introduced by Raisee et al. [1] , that is further extended by introducing sparse polynomial chaos expansions. Specifically, an optimal stochastic basis is calculated from a coarse scale analysis, using proper orthogonal decomposition and sparse polynomial chaos and is then utilized in the fine scale analysis. This way, the computational expense on both the coarse and fine discretization levels is drastically reduced. Two application examples are considered to validate the proposed method and demonstrate its potential in solving high dimensional uncertainty quantification problems. One analytical stochastic problems is first studied, where up to 20 uncertainties were introduced in order to challenge the proposed method. A more realistic CFD type application is then discussed. It consists of a two dimensional NACA 0012 symmetric profile operating at subsonic flight conditions. It is shown that the proposed reduced order method based on sparse polynomial chaos expansions is able to predict statistical quantities with little loss of information, at a cheaper cost than other state-of-the-art techniques. [ABSTRACT FROM AUTHOR]